We propose a model describing liquid-solid phase coexistence in mixed lipid membranes by including explicitly the occurrence of a rippled phase. For a single component membrane, we employ a previous model in which the membrane thickness is used as an order parameter. As function of temperature, this model properly accounts for the phase behavior of the three possible membrane phases: solid, liquid and the rippled phase. Our primary aim is to explore extensions of this model to binary lipid mixtures by considering the composition dependence of important model parameters. The obtained phase diagrams show various liquid, solid and rippled phase coexistence regions, and are in quantitative agreement with the experimental ones for some specific lipid mixtures.